A decision was made early on to use Wwise for the audio solution to enable us to deliver audio at the quality you've received it here. Wwise sadly does not support WebGL.
Oversight on my part (I headed the sound implementation). I work regularly with Wwise but I'm fairly new to publishing on itch -- while the rest of the team has more experience there. I hadn't considered the limitation that would put on us when it came time to publish, and the rest of the team just was not aware until we were far too committed.
All that said, glad to hear you enjoy what that sacrifice enabled us to do! :)